Mathematical Sciences: Harmonic Analysis on Homogeneous Spaces, C*-Algebraic Index Theory

小行星9625336 Lipsman教授和Rosenberg教授计划继续他们各自的 工作在群表示理论，分析齐次空间，和 C*-代数指标理论。 利普曼教授将研究傅立叶 齐性空间的分析，它与不变微分的关系 算子和各种轨道结构，以及分布的概念 Frobenius互惠。 罗森伯格教授将研究流形的积极 标量曲率，流形空间上的指数理论，K-理论， 算子代数的L-理论 Lipsman和Rosenberg教授将 共同研究Paley-Wiener定理和李群的不确定性原理。 这个项目的重点将是分析（例如，偏微分方程的解决方案的研究）和几何结构之间的相互作用，广义解释。 分析与几何的关系是现代几何学研究的重要课题之一 数学和物理。 Lipsman教授和Rosenberg教授还将共同 通过加强通常的多变量微积分课程，强调基本的几何和物理原理的计算机项目，努力帮助传达这一主题给本科生。 ***

9625336 Lipsman Professors Lipsman and Rosenberg plan to continue their respective work in group representation theory, analysis on homogeneous spaces, and C*-algebraic index theory. Professor Lipsman will study the Fourier analysis of homogeneous spaces, its relation to invariant differential operators and various orbital constructs, and the notion of distributional Frobenius reciprocity. Professor Rosenberg will study manifolds of positive scalar curvature, index theory on manifold-like spaces, and K-theory and L-theory of operator algebras. Professors Lipsman and Rosenberg will jointly study Paley-Wiener Theorems and uncertainty principles on Lie groups. The emphasis of this project will be on the interplay between analysis (for example, study of the solutions of partial differential equations) and geometrical structure, broadly interpreted. The relationship between analysis and geometry is one of the most important themes in modern mathematics and physics. Professors Lipsman and Rosenberg will also jointly work to help convey this theme to undergraduates by enhancing the usual multivariable calculus course with computer projects emphasizing the underlying geometrical and physical principles. ***